Suppose there’s a rhombus of side length $5\,\mathrm{cm}$, which is $9\,\mathrm{cm}$ wide (measured parallel to one of the sides). What is the area of the rhombus? Show hint

We must find the height. Can you see a right-angled triangle?

The length of the bottom side is also $5\,\mathrm{cm}$, so the remaining width to the right of that is $4\,\mathrm{cm}$. Since the height $h$ is measured perpendicular to the base, we have a right-angled triangle with hypotenuse $5\,\mathrm{cm}$, and sides $4\,\mathrm{cm}$ and $h$. Therefore, $h = 3\,\mathrm{cm}$, and the area is base times height, which comes to $15\,\mathrm{cm^2}$.